# How do you simplify 5sqrt2 (sqrt8 - sqrt50)?

Jun 6, 2015

The simplified writting is $- 30$

To simplify, you need to write every term as a multiple of $\sqrt{2}$

$5 \sqrt{2} \left(\sqrt{8} - \sqrt{50}\right) = 5 \sqrt{2} \left(\sqrt{2 \cdot 4} - \sqrt{2 \cdot 25}\right)$

$= 5 \sqrt{2} \left(\sqrt{2 \cdot {2}^{2}} - \sqrt{2 \cdot {5}^{2}}\right)$

$= 5 \sqrt{2} \left(2 \sqrt{2} - 5 \sqrt{2}\right)$

$= 5 \sqrt{2} \cdot \left(- 3 \sqrt{2}\right)$

$= \left(5 \cdot \left(- 3\right)\right) \cdot \left(\sqrt{2} \cdot \sqrt{2}\right)$

$= - 15 \cdot 2 = - 30$